Digital communication systems employing bandpass filtered channels typically generate a transmission signal by modulating a carrier signal with digital data prior to transmission. The result of such digital modulation is a time sequence of data samples which are converted by a digital-to-analog converter (DAC) and amplified for transmission.
There are three basic well known techniques for digital modulation, namely, amplitude shift keying (ASK), frequency shift keying (FSK) and phase shift keying (PSK), and numerous variations from these techniques. Waveforms representative of each of these basic techniques are depicted in FIG. 1. It can be seen that each amplitude, frequency or phase in the respective waveforms corresponds to a binary "1" or "0".
It will be understood that if each bit of digital data is used to modulate the carrier signal the amount of data which can be transmitted is limited for a given unit of time. Accordingly, many modulation techniques provide for the transmission of multiple data per unit of time. In more complicated implementations of ASK, FSK and PSK techniques, binary data is grouped, so that a single symbol is assigned to represent a known group of binary data. Each symbol has a corresponding known amplitude, frequency or phase. These more complicated implementations are known as M-ary signaling. For example, in an 8-ary PSK digital modulation scheme, where 8 possible phases are available as symbols, binary data is grouped into sets of 3 bits each. The 8 possible phases can represent 8 possible groups of binary data, e.g., 000, 001, 010, 011, 100, 101, 110, and 111 (see FIG. 2A). Consequently, groups of data are transmitted for a given unit of time.
It is also well known to arrange the possible groups of binary data in a particular digital modulation technique in Gray Code format. The Gray Coding of data groups ensures that only a single-bit differs between consecutive groups. For instance, referring to the 8-ary PSK modulation constellation shown in FIG. 2A, it will be seen that the order of data groups around the constellation is 001, 000, 100, 101, etc. Only one bit differs between each group. Without Gray Coding the symbol order could correspond to the actual numerical sequence, i.e. 000, 001, 010, 011, etc. As is known, the placement of data groups in such Gray Code format reduces the probability of bit error by a decoder following demodulation of the transmitted signal.
As indicated above, the PSK modulation technique symbols can be represented by a phase or modulation constellation. In binary PSK (BPSK) only 2 phases are provided where one phase is designated by a symbol having a bit "0" and the second phase is designated by a symbol having a bit "1". 8-ary PSK and BPSK phase constellations are depicted in FIGS. 2A and 2B respectively. It will be appreciated from FIG. 2 that each symbol can be represented by the complex sequence: EQU x(n)=x.sub.r (n)+x.sub.im (n) (1)
where x.sub.r (n) is a real component and x.sub.im (n) is an imaginary component of signal x(n). Thus, each symbol may have both real and imaginary components. It will be understood that the real components correspond to in-phase components (I) and the imaginary components correspond to quadrature components (Q) of a composite signal.
A typical implementation of an M-ary PSK system is shown in FIG. 3. Binary input data 10 is received by serial-to-parallel converter 12. The serial-to-parallel converter collects the binary data into groups having log.sub.2 M bits. It will be recalled that each group is represented by a symbol and that each symbol includes both real and imaginary components. The real component of each symbol is provided to bandlimiting filter 14 and the imaginary component of each symbol is provided to bandlimiting filter 16. The input data rate is represented as f.sub.b and the symbol or baud rate is represented as f.sub.s where f.sub.s =f.sub.b /log.sub.2 M. The filtered I and Q components are then modulated by mixers 18 and 20, respectively, and added before transmission by adder 22. The modulated output data indicative of each symbol is then transmitted over a fixed interval defined as the symbol period.
Proper detection of a digitally modulated signal, using the PSK technique, requires that a receiver not be subject to discontinuities in the transmitted signal at the symbol boundaries. For this reason the phase change between transmitted symbols is effected gradually by applying bandlimiting filters 14 and 16 to both in-phase (I) and quadrature (Q) phase components. Bandlimiting filters 14 and 16 provide the required spectral shaping, i.e., gradual phase change, to aid in the detection of the transmitted signal. Consequently, in practice the proper phase or symbol is detected only over a portion of the symbol time rather than over the entire symbol time as depicted in FIG. 1.
Bandlimiting filters 14 and 16 are characterized by an impulse response h(n). It will be appreciated that the filter output y(n) is the convolution of h(n) and the filter input x(n). In the frequency domain the response H(.omega.) is generally in the form of a bandpass filter. Thus, its time representation after performing an inverse Fourier transform can be represented generally as follows: EQU sin(.omega..sub.c nt/T)/(.omega..sub.c nt/T).
Since h(n) is of infinite duration it must be truncated to a period T' where T' is typically equal to a number of symbol periods, NT. It is also well known in the art to use a window function, W(.omega.), or w(n) in the time domain, to truncate an impulse response of infinite duration. Therefore, bandlimiting filters can be represented by n impulses over the period T', where each impulse has an amplitude k.sub.n =h(n).times.w(n).
Mixers 18 and 20 which are well known in the art, perform real multiplication of their input signals and produce a desired output together with interharmonic distortion. Thus, carrier frequency and mixer design must be selected so that harmonics produced from the mixer can be eliminated by filtering (not shown in FIG. 3) so as not to distort the transmitted information signal. Often such filters are very complex and costly due to the specifications required to eliminate or reduce interharmonic distortion to an acceptable level.
Intersymbol interference also may distort the transmitted signal. Even though a window can be applied to the bandlimiting filters 14 and 16 to truncate the impulse response, intersymbol interference can still result. Intersymbol interference is caused by selecting a period T' which is greater than the symbol period T. Thus previous symbols contribute to later symbols. For example, if the filter length T' is selected such that T' is 20T, each symbol will have contributions from the last 19 symbols (i.e., 20 symbol periods long). This may be better understood with reference to FIG. 3. The output f(n) is modulated output data and can be defined by the following formula for a sequence of discrete samples derived from the sequence of input symbols x(n): ##EQU1## where S is the number of samples or impulses of the impulse response provided during each symbol period. Thus, the amplitude of the input multiplied by the impulse response for the real and imaginary components are summed for each symbols where they overlap in time which is dependent on the filter length T'.
The results of each stage of the calculation can be seen in FIGS. 4a to 4c. FIG. 4a shows the symbols as output from the serial-to-parallel converter 12 at the baud rate. Note that the output sample rate may be greater than the symbol rate. The output of bandlimiting filter 14 or 16 (i.e., only one component of the complex input is depicted) is shown in FIG. 4b. FIG. 4c, then depicts the modulated signal after the outputs of each symbol have been summed where they overlap in time. For instance, the sum of the amplitudes ".times.", ".DELTA." and ".quadrature." shown at a time designated 15 in FIG. 4b would result in the amplitude of the modulated carrier shown at 17 in FIG. 4c.
As previously indicated, mixers 18 and 20 can introduce harmonics which must be removed. Generally such harmonics are removed through the use of baseband transmit filters. Implementing baseband transmit filters has several drawbacks. Depending on the specific design requirements, lumped-element analog filters, probably the most prevalent filter type, often require months of development, empirical design methods, and individual factory tuning and consequently are costly. Analog Finite Impulse Response (FIR) filters have similar restrictions. Digital FIR filters that use multipliers are still relatively expensive, can consume substantial power and are limited to low-speed operation (multiplication cycle times typically greater than 100 ns). Switched capacitor filters, though efficient in terms of both silicon area and power consumption are limited to very low-speed data communications commonly two-kilobaud voiceband modems. Older Binary Transversal Filters (BTFs) that use resistive register networks share many of the same limitations as analog lumped-element and FIR filters, while the newer BTFs or direct-addressing FIR filters can be awkward to fabricate for high-level modulation or alternatively require distinct summing networks.
It has been suggested, [C. A. Siller, Jr. et al., Spectral Shaping and Digital Synthesis of an M-ary Time Series, IEEE Communications Magazine, February 1989, pp. 15-24.], that such problems may be overcome by storing in advance the impulse response data, i.e., data representing the output of the filters y(n) for each of the possible M symbols of the modulation filters in a PROM (programmable read only memory) and using an address generator to generate the appropriate address based on the input symbol to create the corresponding sampled output for each symbol. However, such systems have been ineffective in dealing with intersymbol interference. For instance, Siller disclosed generating a number of symbol sequences a priori and computing the outputs based on each sequence to account for the intersymbol interference. Such a system places a heavy burden on memory requirements which grow linearly with the number of samples to be represented in a symbol period T and exponentially with both M, the number of possible symbols, and the filter length NT. Alternatively, such a design limits the number of samples represented during symbol period T, the number of possible symbols M, and the filter length NT, thereby reducing the accuracy of the transmitted signal and reducing the possible modulation schemes.
Furthermore, previous digital modulators have not provided versatility for additional possible modulation schemes. For instance, a new system must be designed each time a parameter is changed (e.g., input bit rate, baud rate, etc.). Likewise, previous digital modulators have not been capable of providing high-speed data rates with accuracy without greatly limiting the complexity of the modulation scheme.
Consequently, a need exists for a digital modulator which overcomes the difficulties of modulators incorporating bandlimited filters and which are versatile enough to accommodate new modulation schemes.